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The Bethe–Slater curve is a
Open Quantum Materials Database
The Bethe–Slater curve is a heuristic
A heuristic (; ), or heuristic technique, is any approach to problem solving or self-discovery that employs a practical method that is not guaranteed to be optimal, perfect, or rational, but is nevertheless sufficient for reaching an immediate, ...
explanation for why certain metals are ferromagnetic
Ferromagnetism is a property of certain materials (such as iron) which results in a large observed magnetic permeability, and in many cases a large magnetic coercivity allowing the material to form a permanent magnet. Ferromagnetic materials ...
and others are antiferromagnetic
In materials that exhibit antiferromagnetism, the magnetic moments of atoms or molecules, usually related to the spins of electrons, align in a regular pattern with neighboring spins (on different sublattices) pointing in opposite directions. ...
. It assumes a Heisenberg model of magnetism, and explains the differences in exchange energy
In chemistry and physics, the exchange interaction (with an exchange energy and exchange term) is a quantum mechanical effect that only occurs between identical particles. Despite sometimes being called an exchange force in an analogy to classica ...
of transition metals
In chemistry, a transition metal (or transition element) is a chemical element in the d-block of the periodic table (groups 3 to 12), though the elements of group 12 (and less often group 3) are sometimes excluded. They are the elements that can ...
as due to the ratio of the interatomic distance ''a'' to the radius ''r'' of the ''3d'' electron shell
In chemistry and atomic physics, an electron shell may be thought of as an orbit followed by electrons around an atom's nucleus. The closest shell to the nucleus is called the "1 shell" (also called the "K shell"), followed by the "2 shell" (o ...
. When the magnetically important ''3d'' electrons of adjacent atoms are relatively close to each other, the exchange interaction, , is negative, but when they are further away, the exchange interaction becomes positive, before slowly dropping off.
The idea of relating exchange energy to inter-atomic distance was first proposed by John C. Slater
John Clarke Slater (December 22, 1900 – July 25, 1976) was a noted American physicist who made major contributions to the theory of the electronic structure of atoms, molecules and solids. He also made major contributions to microwave electroni ...
in 1930, and illustrated as a curve on a graph in a review by Sommerfeld
Arnold Johannes Wilhelm Sommerfeld, (; 5 December 1868 – 26 April 1951) was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and mentored many students for the new era of theoretica ...
and Bethe in 1933.
For a pair of atoms, the exchange interaction ''wij'' (responsible for the energy ''E'') is calculated as:Soshin Chikazumi, Physics of Ferromagnetism, Oxford University Press, New York, 1997, p. 125,
where: = exchange integral; ''S'' = electron spins; ''i'' and ''j'' = indices of the two atoms.
The Slater curve does produce realistic results, predicting Iron, Cobalt and Nickel to be the elements with ferromagnetic ordering. The curve is of practical use as a simple way of estimating based on the average atomic separation. However, more recent evaluations with realistic calculations of the exchange interactions show significantly more complex physics when treating the interactions of different atomic orbitals in an atom separately, rather than as a single unit.
External links
Open Quantum Materials Database
References
{{DEFAULTSORT:Bethe-Slater curve Magnetic exchange interactions Ferromagnetism